Problem: What number could replace $k$ below? $\dfrac{1}{10} = \dfrac{10}{k}$
Solution: The fraction on the left represents 1 out of 10 slices of a rectangular cake. How many total slices would we need if we want the same amount of cake in 10 slices? We would need to cut the cake into 100 slices. $\dfrac{1}{10} = \dfrac{10}{100}$ and so the answer is $100$ Another way to get the answer is to multiply by $\dfrac{10}{10}$ $\dfrac{10}{10} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{10} \times \dfrac{10}{10} = \dfrac{10}{100} $ so our answer is $100$.